5. n=1 I> Let Ω ⊆ C be open. Let {fn}∞ be a sequence of functions in H(Ω). Suppose that f : Ω → C and fn → f uniformly on compact subsets of Ω. Show that f ∈ H(Ω).




5.

















n=1




I> Let Ω
⊆
C be open. Let
{
f
n
}
∞




be a sequence of functions in
H(Ω). Suppose that





f
: Ω
→
C and
f
n

→

f
uniformly on compact subsets of Ω. Show that
f

∈

H(Ω).





May 12, 2022
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